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Relaxation of energy and approximate Riemann solvers for general pressure laws in fluid dynamics. (English) Zbl 0960.76051
The authors study compressible Euler equations with a general pressure law \(p(\rho,\varepsilon)\), where \(\rho\) is the fluid density, and \(\varepsilon\) denotes its specific internal energy. The key idea is to employ the Chapman-Enskog expansion to derive an additive energy decomposition \(\varepsilon= \varepsilon_1+\varepsilon_2\), where the internal energy \(\varepsilon_1\) is associated with a simpler pressure law \(p_1(\rho,\varepsilon_1)\), and the energy \(\varepsilon_2\) is advected by the flow. Then these two energies are calculated by a relaxation procedure, and in the limit of infinite relaxation rate, the authors arrive at the initial pressure law. As an illustration, this quite general procedure is applied to approximate finite volume Riemann solvers for polytropic gases with simple advection, based on Godunov and Roe-type schemes.

76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
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